Until about 20 years ago, kiwi fruit, with its lovely green color, was an expensive imported fruit from New Zealand. Kiwis are now grown extensively in California so it is widely available in the summer and it is very affordable.
1. Cook chicken in a vegetable steamer until cooked through, 10 to 12 minutes. Transfer chicken to a plate and set aside to cool. When cool enough to handle, cut chicken into slices, reserving any juices that have collected on plate.
2. In a small bowl, combine lime zest, lime juice, honey, soy sauce, ginger, and any reserved chicken juices. Pour 1/3 cup of this dressing over chicken slices and set aside to marinate at least one hour.
3. Line individual serving plates with shredded lettuce. Arrange kiwi and water chestnut slices around outside, mound chicken in center and sprinkle with scallions. Drizzle remaining dressing over salad.